Correction: A prior version of this story incorrectly attributed a quote to Sen. McCain.

WASHINGTON — Two leading senators announced a bipartisan deal Thursday to address growing concerns about veterans' ability to seek medical care at VA facilities nationwide. The legislation could get a vote as early as next week.

Senate Veterans Affairs Committee Chairman Bernie Sanders, I-Vt., and Sen. John McCain, R-Ariz., a Vietnam War veteran, announced the compromise on the Senate floor. The bill is in response to a recent preliminary investigation that found systemic problems with VA staff delaying medical care for veterans and manipulating records to hide those delays.

The growing controversy, which is still under investigation, caused the resignation last week of Veterans Affairs Secretary Eric Shinseki.

The Sanders-McCain legislation addresses the short-term problem of access to care by authorizing a two-year trial program that would allow veterans to seek private health care if they reside more than 40 miles from a VA facility or have been waiting more than 30 days for treatment. Long-term, the legislation authorizes the construction of 26 medical facilities in 18 states, and directs $500 million in unspent funds to hire more doctors and other health-care providers.

The package also includes provisions to provide better treatment for victims of sexual assault, as well as an unrelated but popular provision to help veterans pay for college by allowing them to pay in-state tuition rates.

"Reaching a compromise among people who look at the world very different is not easy," Sanders said. "But right now we have a crisis on our hands and it is imperative that we deal with that crisis."

The two senators had released competing proposals this week. Their ability to reach a compromise so quickly underscores how seriously Congress is taking the controversy.

McCain publicly called on senators to not block a vote on the package. "We would like to have your commitment to seeing this thing through to the president's desk," McCain said.

The Senate could take up the bill as early as next week.

The U.S. House is not in session this week, but there is much in the Senate package for House Republicans to support. The Sanders-McCain bill includes a House-passed provision that would grant the VA secretary greater authority to fire senior executives. Sen. Marco Rubio, R-Fla., who had introduced a mirror provision in the Senate, lauded the package, which has the support of veterans' groups.

"Considering the deep debt of gratitude our nation owes our veterans, I'm optimistic that the Senate will soon join the U.S. House of Representatives and pass these important reforms," Rubio said.

Meanwhile, President Obama's pick to be the top health official at the VA withdrew himself from consideration on Thursday, citing concerns about a prolonged Senate confirmation battle. Jeffrey Murawsky runs the VA's Chicago regional office and he was nominated last month to become the new undersecretary for health care. Obama accepted Murawsky's withdrawal and the White House is seeking another candidate. The position oversees the VA's 9 million patients,150 hospitals and 820 walk-in clinics.

Obama last week tapped Sloan Gibson to serve as acting VA secretary following Shinseki's resignation while the White House seeks a nominee, who must be confirmed by the U.S. Senate.